Bring water and rice to a boil in a saucepan. Reduce heat to medium-low, cover, and simmer until rice is tender and water has been absorbed, 20 to 25 minutes.
Place tomatoes in a pot with water to cover. Bring to a boil and cook until soft but not falling apart, 5 to 8 minutes. Drain and let cool briefly. Peel and place in a blender; add onion, chipotle peppers, garlic, and black pepper. Blend until smooth. Strain mixture, discarding solids, for the sauce.
Heat oil in a saucepan over medium-high heat. Add carrots and celery; saute until lightly browned, about 5 minutes. Pour in blended tomato sauce. Add chicken broth and bouillon. Cook and stir until carrot and celery are soft, 10 to 15 minutes. Add peas and chicken breast; cook until heated through, about 3 minutes. Serve soup over a spoonful of rice; top with avocado slices and Monterey Jack cheese.